Question

the projected percent of a countrys adult population with diabetes (diagnosed and undiagnosed) can be modeled by ( y = 7.97x^{0.496} ), where ( x ) is the number of years after 2000. complete parts (a)-(c).
a) does this model indicate that the percent of a countrys adult population with diabetes is projected to increase or decrease?
increase
decrease
b) what percent is projected for 2018?

Explanation:

Step1: Find the value of \(x\) for 2018

Since \(x\) is the number of years after 2000, for 2018, \(x = 2018 - 2000=18\).

Step2: Substitute \(x = 18\) into the model \(y = 7.97x^{0.496}\)

We get \(y=7.97\times18^{0.496}\).
First, calculate \(18^{0.496}\). Using a calculator, \(18^{0.496}\approx3.85\).
Then, \(y = 7.97\times3.85\approx30.68\).

Answer:

\(30.68\)